Existence and multiplicity of $a$-harmonic solutions for a Steklov problem with variable exponents
| Autor: | Abdellah Ahmed Zerouali, Belhadj Karim, Omar Chakrone |
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| Jazyk: | English<br />Portuguese |
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Boletim da Sociedade Paranaense de Matemática, Vol 36, Iss 2 (2018) |
| Druh dokumentu: | article |
| ISSN: | 0037-8712 2175-1188 |
| DOI: | 10.5269/bspm.v36i2.31071 |
| Popis: | Using variational methods, we prove in a different cases the existence and multiplicity of $a$-harmonic solutions for the following elleptic problem:\begin{equation*}\begin{gathered}div(a(x, \nabla u))=0, \quad \text{in }\Omega, \\a(x, \nabla u).\nu=f(x,u), \quad \text{on } \partial\Omega,\end{gathered}\end{equation*} where $\Omega\subset\mathbb{R}^N(N \geq 2)$ is a bounded domain ofsmooth boundary $\partial\Omega$ and $\nu$ is the outward normalvector on $\partial\Omega$. $f: \partial\Omega\times \mathbb{R} \rightarrow \mathbb{R},$ $a: \overline{\Omega}\times \mathbb{R}^{N} \rightarrow\mathbb{R}^{N},$ are fulfilling appropriate conditions. |
| Databáze: | Directory of Open Access Journals |
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